Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.4% → 82.9%

Time: 35.9s

Alternatives: 28

Speedup: 0.5×

• 58.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;\left(t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot t_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(b, \mathsf{fma}\left(i, t, z \cdot \left(-c\right)\right), \mathsf{fma}\left(j, t_2, t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(a \cdot \left(c \cdot j - x \cdot t\right)\right)}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (- (* a c) (* y i))))
   (if (<= (+ (+ t_1 (* b (- (* t i) (* z c)))) (* j t_2)) INFINITY)
     (fma b (fma i t (* z (- c))) (fma j t_2 t_1))
     (cbrt (pow (* a (- (* c j) (* x t))) 3.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if (((t_1 + (b * ((t * i) - (z * c)))) + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(b, fma(i, t, (z * -c)), fma(j, t_2, t_1));
	} else {
		tmp = cbrt(pow((a * ((c * j) - (x * t))), 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * t_2)) <= Inf)
		tmp = fma(b, fma(i, t, Float64(z * Float64(-c))), fma(j, t_2, t_1));
	else
		tmp = cbrt((Float64(a * Float64(Float64(c * j) - Float64(x * t))) ^ 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(b * N[(i * t + N[(z * (-c)), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2 + t$95$1), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 89.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 89.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 89.0%

         \[\leadsto \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - \color{blue}{t \cdot i}\right) \]

      2. cancel-sign-sub-inv 89.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. *-commutative 89.0%

         \[\leadsto \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \color{blue}{\left(c \cdot z - t \cdot i\right) \cdot \left(-b\right)} \]

      4. +-commutative 89.0%

         \[\leadsto \color{blue}{\left(c \cdot z - t \cdot i\right) \cdot \left(-b\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]

      5. distribute-rgt-neg-out 89.0%

         \[\leadsto \color{blue}{\left(-\left(c \cdot z - t \cdot i\right) \cdot b\right)} + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      6. *-commutative 89.0%

         \[\leadsto \left(-\color{blue}{b \cdot \left(c \cdot z - t \cdot i\right)}\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      7. distribute-rgt-neg-in 89.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) \]

      8. fma-udef 89.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]

   4. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(i, t, c \cdot \left(-z\right)\right), \mathsf{fma}\left(j, c \cdot a - i \cdot y, x \cdot \left(z \cdot y - t \cdot a\right)\right)\right)} \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 61.0%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a \cdot \left(c \cdot j - t \cdot x\right)\right) \cdot \left(a \cdot \left(c \cdot j - t \cdot x\right)\right)\right) \cdot \left(a \cdot \left(c \cdot j - t \cdot x\right)\right)}} \]

      2. pow3 61.0%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(a \cdot \left(c \cdot j - t \cdot x\right)\right)}^{3}}} \]

      3. *-commutative 61.0%

         \[\leadsto \sqrt[3]{{\left(a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right)\right)}^{3}} \]

   6. Applied egg-rr 61.0%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(a \cdot \left(j \cdot c - t \cdot x\right)\right)}^{3}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(b, \mathsf{fma}\left(i, t, z \cdot \left(-c\right)\right), \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(a \cdot \left(c \cdot j - x \cdot t\right)\right)}^{3}}\\ \end{array} \]

Alternative 2: 82.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;t_1 + j \cdot t_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t_2, t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(a \cdot \left(c \cdot j - x \cdot t\right)\right)}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (- (* a c) (* y i))))
   (if (<= (+ t_1 (* j t_2)) INFINITY)
     (fma j t_2 t_1)
     (cbrt (pow (* a (- (* c j) (* x t))) 3.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = cbrt(pow((a * ((c * j) - (x * t))), 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(t_1 + Float64(j * t_2)) <= Inf)
		tmp = fma(j, t_2, t_1);
	else
		tmp = cbrt((Float64(a * Float64(Float64(c * j) - Float64(x * t))) ^ 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[Power[N[Power[N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 89.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 89.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 89.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 61.0%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a \cdot \left(c \cdot j - t \cdot x\right)\right) \cdot \left(a \cdot \left(c \cdot j - t \cdot x\right)\right)\right) \cdot \left(a \cdot \left(c \cdot j - t \cdot x\right)\right)}} \]

      2. pow3 61.0%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(a \cdot \left(c \cdot j - t \cdot x\right)\right)}^{3}}} \]

      3. *-commutative 61.0%

         \[\leadsto \sqrt[3]{{\left(a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right)\right)}^{3}} \]

   6. Applied egg-rr 61.0%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(a \cdot \left(j \cdot c - t \cdot x\right)\right)}^{3}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(a \cdot \left(c \cdot j - x \cdot t\right)\right)}^{3}}\\ \end{array} \]

Alternative 3: 82.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;t_1 + j \cdot t_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t_2, t_1\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (- (* a c) (* y i))))
   (if (<= (+ t_1 (* j t_2)) INFINITY)
     (fma j t_2 t_1)
     (* a (- (* c j) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(t_1 + Float64(j * t_2)) <= Inf)
		tmp = fma(j, t_2, t_1);
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 89.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 89.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 89.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 4: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* a (- (* c j) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 89.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 5: 47.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+178}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.8e+118)
     t_2
     (if (<= b -7.8e+39)
       t_1
       (if (<= b -3e-41)
         (* i (* j (- y)))
         (if (<= b 9e-182)
           t_1
           (if (<= b 3.5e-56)
             (* x (* y z))
             (if (<= b 2.75e+16)
               t_1
               (if (<= b 6.6e+65)
                 t_2
                 (if (<= b 2.7e+115)
                   t_1
                   (if (<= b 2.4e+178) (* c (* z (- b))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e+118) {
		tmp = t_2;
	} else if (b <= -7.8e+39) {
		tmp = t_1;
	} else if (b <= -3e-41) {
		tmp = i * (j * -y);
	} else if (b <= 9e-182) {
		tmp = t_1;
	} else if (b <= 3.5e-56) {
		tmp = x * (y * z);
	} else if (b <= 2.75e+16) {
		tmp = t_1;
	} else if (b <= 6.6e+65) {
		tmp = t_2;
	} else if (b <= 2.7e+115) {
		tmp = t_1;
	} else if (b <= 2.4e+178) {
		tmp = c * (z * -b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.8d+118)) then
        tmp = t_2
    else if (b <= (-7.8d+39)) then
        tmp = t_1
    else if (b <= (-3d-41)) then
        tmp = i * (j * -y)
    else if (b <= 9d-182) then
        tmp = t_1
    else if (b <= 3.5d-56) then
        tmp = x * (y * z)
    else if (b <= 2.75d+16) then
        tmp = t_1
    else if (b <= 6.6d+65) then
        tmp = t_2
    else if (b <= 2.7d+115) then
        tmp = t_1
    else if (b <= 2.4d+178) then
        tmp = c * (z * -b)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e+118) {
		tmp = t_2;
	} else if (b <= -7.8e+39) {
		tmp = t_1;
	} else if (b <= -3e-41) {
		tmp = i * (j * -y);
	} else if (b <= 9e-182) {
		tmp = t_1;
	} else if (b <= 3.5e-56) {
		tmp = x * (y * z);
	} else if (b <= 2.75e+16) {
		tmp = t_1;
	} else if (b <= 6.6e+65) {
		tmp = t_2;
	} else if (b <= 2.7e+115) {
		tmp = t_1;
	} else if (b <= 2.4e+178) {
		tmp = c * (z * -b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.8e+118:
		tmp = t_2
	elif b <= -7.8e+39:
		tmp = t_1
	elif b <= -3e-41:
		tmp = i * (j * -y)
	elif b <= 9e-182:
		tmp = t_1
	elif b <= 3.5e-56:
		tmp = x * (y * z)
	elif b <= 2.75e+16:
		tmp = t_1
	elif b <= 6.6e+65:
		tmp = t_2
	elif b <= 2.7e+115:
		tmp = t_1
	elif b <= 2.4e+178:
		tmp = c * (z * -b)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.8e+118)
		tmp = t_2;
	elseif (b <= -7.8e+39)
		tmp = t_1;
	elseif (b <= -3e-41)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (b <= 9e-182)
		tmp = t_1;
	elseif (b <= 3.5e-56)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 2.75e+16)
		tmp = t_1;
	elseif (b <= 6.6e+65)
		tmp = t_2;
	elseif (b <= 2.7e+115)
		tmp = t_1;
	elseif (b <= 2.4e+178)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.8e+118)
		tmp = t_2;
	elseif (b <= -7.8e+39)
		tmp = t_1;
	elseif (b <= -3e-41)
		tmp = i * (j * -y);
	elseif (b <= 9e-182)
		tmp = t_1;
	elseif (b <= 3.5e-56)
		tmp = x * (y * z);
	elseif (b <= 2.75e+16)
		tmp = t_1;
	elseif (b <= 6.6e+65)
		tmp = t_2;
	elseif (b <= 2.7e+115)
		tmp = t_1;
	elseif (b <= 2.4e+178)
		tmp = c * (z * -b);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+118], t$95$2, If[LessEqual[b, -7.8e+39], t$95$1, If[LessEqual[b, -3e-41], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-182], t$95$1, If[LessEqual[b, 3.5e-56], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.75e+16], t$95$1, If[LessEqual[b, 6.6e+65], t$95$2, If[LessEqual[b, 2.7e+115], t$95$1, If[LessEqual[b, 2.4e+178], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.80000000000000032e118 or 2.75e16 < b < 6.60000000000000046e65 or 2.4e178 < b

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 77.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -5.80000000000000032e118 < b < -7.8000000000000002e39 or -2.99999999999999989e-41 < b < 8.9999999999999998e-182 or 3.4999999999999998e-56 < b < 2.75e16 or 6.60000000000000046e65 < b < 2.70000000000000004e115

   1. Initial program 63.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 58.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 58.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -7.8000000000000002e39 < b < -2.99999999999999989e-41

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 65.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 65.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 65.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 65.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 65.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 65.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around 0 48.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.1%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 48.1%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   7. Simplified 48.1%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if 8.9999999999999998e-182 < b < 3.4999999999999998e-56

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 58.8%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 58.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 48.0%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 48.0%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 2.70000000000000004e115 < b < 2.4e178

   1. Initial program 58.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 42.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 42.1%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 42.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in z around inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 42.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 42.9%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   7. Simplified 42.9%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-neg-out 42.9%

         \[\leadsto \color{blue}{-b \cdot \left(z \cdot c\right)} \]

      2. add-sqr-sqrt 42.7%

         \[\leadsto -\color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot \left(z \cdot c\right) \]

      3. sqrt-unprod 35.0%

         \[\leadsto -\color{blue}{\sqrt{b \cdot b}} \cdot \left(z \cdot c\right) \]

      4. sqr-neg 35.0%

         \[\leadsto -\sqrt{\color{blue}{\left(-b\right) \cdot \left(-b\right)}} \cdot \left(z \cdot c\right) \]

      5. sqrt-unprod 0.0%

         \[\leadsto -\color{blue}{\left(\sqrt{-b} \cdot \sqrt{-b}\right)} \cdot \left(z \cdot c\right) \]

      6. add-sqr-sqrt 25.4%

         \[\leadsto -\color{blue}{\left(-b\right)} \cdot \left(z \cdot c\right) \]

      7. associate-*r* 25.4%

         \[\leadsto -\color{blue}{\left(\left(-b\right) \cdot z\right) \cdot c} \]

      8. add-sqr-sqrt 0.0%

         \[\leadsto -\left(\color{blue}{\left(\sqrt{-b} \cdot \sqrt{-b}\right)} \cdot z\right) \cdot c \]

      9. sqrt-unprod 43.0%

         \[\leadsto -\left(\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}} \cdot z\right) \cdot c \]

      10. sqr-neg 43.0%

          \[\leadsto -\left(\sqrt{\color{blue}{b \cdot b}} \cdot z\right) \cdot c \]

      11. sqrt-unprod 58.3%

          \[\leadsto -\left(\color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot z\right) \cdot c \]

      12. add-sqr-sqrt 58.6%

          \[\leadsto -\left(\color{blue}{b} \cdot z\right) \cdot c \]

   9. Applied egg-rr 58.6%

      \[\leadsto \color{blue}{-\left(b \cdot z\right) \cdot c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+178}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 6: 67.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) - t_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+120}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+138}:\\ \;\;\;\;t_3 - t_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* y i) (* a c))))
        (t_2 (- (* x (- (* y z) (* t a))) t_1))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -7.2e+120)
     t_3
     (if (<= b 2.4e+37)
       t_2
       (if (<= b 4.7e+138) (- t_3 t_1) (if (<= b 1.1e+172) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((y * i) - (a * c));
	double t_2 = (x * ((y * z) - (t * a))) - t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.2e+120) {
		tmp = t_3;
	} else if (b <= 2.4e+37) {
		tmp = t_2;
	} else if (b <= 4.7e+138) {
		tmp = t_3 - t_1;
	} else if (b <= 1.1e+172) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((y * i) - (a * c))
    t_2 = (x * ((y * z) - (t * a))) - t_1
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-7.2d+120)) then
        tmp = t_3
    else if (b <= 2.4d+37) then
        tmp = t_2
    else if (b <= 4.7d+138) then
        tmp = t_3 - t_1
    else if (b <= 1.1d+172) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((y * i) - (a * c));
	double t_2 = (x * ((y * z) - (t * a))) - t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.2e+120) {
		tmp = t_3;
	} else if (b <= 2.4e+37) {
		tmp = t_2;
	} else if (b <= 4.7e+138) {
		tmp = t_3 - t_1;
	} else if (b <= 1.1e+172) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((y * i) - (a * c))
	t_2 = (x * ((y * z) - (t * a))) - t_1
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7.2e+120:
		tmp = t_3
	elif b <= 2.4e+37:
		tmp = t_2
	elif b <= 4.7e+138:
		tmp = t_3 - t_1
	elif b <= 1.1e+172:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(y * i) - Float64(a * c)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1)
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.2e+120)
		tmp = t_3;
	elseif (b <= 2.4e+37)
		tmp = t_2;
	elseif (b <= 4.7e+138)
		tmp = Float64(t_3 - t_1);
	elseif (b <= 1.1e+172)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((y * i) - (a * c));
	t_2 = (x * ((y * z) - (t * a))) - t_1;
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.2e+120)
		tmp = t_3;
	elseif (b <= 2.4e+37)
		tmp = t_2;
	elseif (b <= 4.7e+138)
		tmp = t_3 - t_1;
	elseif (b <= 1.1e+172)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+120], t$95$3, If[LessEqual[b, 2.4e+37], t$95$2, If[LessEqual[b, 4.7e+138], N[(t$95$3 - t$95$1), $MachinePrecision], If[LessEqual[b, 1.1e+172], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.20000000000000031e120 or 1.1000000000000001e172 < b

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 82.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -7.20000000000000031e120 < b < 2.4e37 or 4.6999999999999998e138 < b < 1.1000000000000001e172

   1. Initial program 68.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0 74.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if 2.4e37 < b < 4.6999999999999998e138

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 69.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 69.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 7: 48.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{+65} \lor \neg \left(b \leq 10^{+172}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.8e+118)
     t_2
     (if (<= b -6.6e+38)
       t_1
       (if (<= b -3e-41)
         (* i (* j (- y)))
         (if (<= b 7e-182)
           t_1
           (if (<= b 3.9e-56)
             (* x (* y z))
             (if (<= b 5e+16)
               t_1
               (if (or (<= b 6.9e+65) (not (<= b 1e+172)))
                 t_2
                 (* c (- (* a j) (* z b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e+118) {
		tmp = t_2;
	} else if (b <= -6.6e+38) {
		tmp = t_1;
	} else if (b <= -3e-41) {
		tmp = i * (j * -y);
	} else if (b <= 7e-182) {
		tmp = t_1;
	} else if (b <= 3.9e-56) {
		tmp = x * (y * z);
	} else if (b <= 5e+16) {
		tmp = t_1;
	} else if ((b <= 6.9e+65) || !(b <= 1e+172)) {
		tmp = t_2;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.8d+118)) then
        tmp = t_2
    else if (b <= (-6.6d+38)) then
        tmp = t_1
    else if (b <= (-3d-41)) then
        tmp = i * (j * -y)
    else if (b <= 7d-182) then
        tmp = t_1
    else if (b <= 3.9d-56) then
        tmp = x * (y * z)
    else if (b <= 5d+16) then
        tmp = t_1
    else if ((b <= 6.9d+65) .or. (.not. (b <= 1d+172))) then
        tmp = t_2
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e+118) {
		tmp = t_2;
	} else if (b <= -6.6e+38) {
		tmp = t_1;
	} else if (b <= -3e-41) {
		tmp = i * (j * -y);
	} else if (b <= 7e-182) {
		tmp = t_1;
	} else if (b <= 3.9e-56) {
		tmp = x * (y * z);
	} else if (b <= 5e+16) {
		tmp = t_1;
	} else if ((b <= 6.9e+65) || !(b <= 1e+172)) {
		tmp = t_2;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.8e+118:
		tmp = t_2
	elif b <= -6.6e+38:
		tmp = t_1
	elif b <= -3e-41:
		tmp = i * (j * -y)
	elif b <= 7e-182:
		tmp = t_1
	elif b <= 3.9e-56:
		tmp = x * (y * z)
	elif b <= 5e+16:
		tmp = t_1
	elif (b <= 6.9e+65) or not (b <= 1e+172):
		tmp = t_2
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.8e+118)
		tmp = t_2;
	elseif (b <= -6.6e+38)
		tmp = t_1;
	elseif (b <= -3e-41)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (b <= 7e-182)
		tmp = t_1;
	elseif (b <= 3.9e-56)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 5e+16)
		tmp = t_1;
	elseif ((b <= 6.9e+65) || !(b <= 1e+172))
		tmp = t_2;
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.8e+118)
		tmp = t_2;
	elseif (b <= -6.6e+38)
		tmp = t_1;
	elseif (b <= -3e-41)
		tmp = i * (j * -y);
	elseif (b <= 7e-182)
		tmp = t_1;
	elseif (b <= 3.9e-56)
		tmp = x * (y * z);
	elseif (b <= 5e+16)
		tmp = t_1;
	elseif ((b <= 6.9e+65) || ~((b <= 1e+172)))
		tmp = t_2;
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+118], t$95$2, If[LessEqual[b, -6.6e+38], t$95$1, If[LessEqual[b, -3e-41], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-182], t$95$1, If[LessEqual[b, 3.9e-56], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+16], t$95$1, If[Or[LessEqual[b, 6.9e+65], N[Not[LessEqual[b, 1e+172]], $MachinePrecision]], t$95$2, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.80000000000000032e118 or 5e16 < b < 6.9e65 or 1.0000000000000001e172 < b

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 78.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -5.80000000000000032e118 < b < -6.5999999999999998e38 or -2.99999999999999989e-41 < b < 6.99999999999999966e-182 or 3.9e-56 < b < 5e16

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 57.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 57.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 57.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 57.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 57.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -6.5999999999999998e38 < b < -2.99999999999999989e-41

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 65.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 65.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 65.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 65.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 65.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 65.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around 0 48.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.1%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 48.1%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   7. Simplified 48.1%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if 6.99999999999999966e-182 < b < 3.9e-56

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 58.8%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 58.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 48.0%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 48.0%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 6.9e65 < b < 1.0000000000000001e172

   1. Initial program 62.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf 56.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   4. Simplified 56.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{+65} \lor \neg \left(b \leq 10^{+172}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 8: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-296}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -3e+95)
     t_3
     (if (<= b -1.32e-41)
       t_1
       (if (<= b -1.4e-296)
         (* a (- (* c j) (* x t)))
         (if (<= b 4.8e-226)
           t_2
           (if (<= b 5e-194)
             t_1
             (if (<= b 3.1e-31)
               t_2
               (if (<= b 1.95e+68)
                 t_1
                 (if (<= b 9.5e+171) (* c (- (* a j) (* z b))) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3e+95) {
		tmp = t_3;
	} else if (b <= -1.32e-41) {
		tmp = t_1;
	} else if (b <= -1.4e-296) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 4.8e-226) {
		tmp = t_2;
	} else if (b <= 5e-194) {
		tmp = t_1;
	} else if (b <= 3.1e-31) {
		tmp = t_2;
	} else if (b <= 1.95e+68) {
		tmp = t_1;
	} else if (b <= 9.5e+171) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-3d+95)) then
        tmp = t_3
    else if (b <= (-1.32d-41)) then
        tmp = t_1
    else if (b <= (-1.4d-296)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 4.8d-226) then
        tmp = t_2
    else if (b <= 5d-194) then
        tmp = t_1
    else if (b <= 3.1d-31) then
        tmp = t_2
    else if (b <= 1.95d+68) then
        tmp = t_1
    else if (b <= 9.5d+171) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3e+95) {
		tmp = t_3;
	} else if (b <= -1.32e-41) {
		tmp = t_1;
	} else if (b <= -1.4e-296) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 4.8e-226) {
		tmp = t_2;
	} else if (b <= 5e-194) {
		tmp = t_1;
	} else if (b <= 3.1e-31) {
		tmp = t_2;
	} else if (b <= 1.95e+68) {
		tmp = t_1;
	} else if (b <= 9.5e+171) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3e+95:
		tmp = t_3
	elif b <= -1.32e-41:
		tmp = t_1
	elif b <= -1.4e-296:
		tmp = a * ((c * j) - (x * t))
	elif b <= 4.8e-226:
		tmp = t_2
	elif b <= 5e-194:
		tmp = t_1
	elif b <= 3.1e-31:
		tmp = t_2
	elif b <= 1.95e+68:
		tmp = t_1
	elif b <= 9.5e+171:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3e+95)
		tmp = t_3;
	elseif (b <= -1.32e-41)
		tmp = t_1;
	elseif (b <= -1.4e-296)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 4.8e-226)
		tmp = t_2;
	elseif (b <= 5e-194)
		tmp = t_1;
	elseif (b <= 3.1e-31)
		tmp = t_2;
	elseif (b <= 1.95e+68)
		tmp = t_1;
	elseif (b <= 9.5e+171)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3e+95)
		tmp = t_3;
	elseif (b <= -1.32e-41)
		tmp = t_1;
	elseif (b <= -1.4e-296)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 4.8e-226)
		tmp = t_2;
	elseif (b <= 5e-194)
		tmp = t_1;
	elseif (b <= 3.1e-31)
		tmp = t_2;
	elseif (b <= 1.95e+68)
		tmp = t_1;
	elseif (b <= 9.5e+171)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+95], t$95$3, If[LessEqual[b, -1.32e-41], t$95$1, If[LessEqual[b, -1.4e-296], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e-226], t$95$2, If[LessEqual[b, 5e-194], t$95$1, If[LessEqual[b, 3.1e-31], t$95$2, If[LessEqual[b, 1.95e+68], t$95$1, If[LessEqual[b, 9.5e+171], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.99999999999999991e95 or 9.49999999999999924e171 < b

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 79.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -2.99999999999999991e95 < b < -1.3200000000000001e-41 or 4.7999999999999999e-226 < b < 5.0000000000000002e-194 or 3.1e-31 < b < 1.95000000000000009e68

   1. Initial program 64.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf 58.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) \]

   4. Simplified 58.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

   if -1.3200000000000001e-41 < b < -1.4e-296

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 64.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 64.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -1.4e-296 < b < 4.7999999999999999e-226 or 5.0000000000000002e-194 < b < 3.1e-31

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 64.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 64.8%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 64.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   if 1.95000000000000009e68 < b < 9.49999999999999924e171

   1. Initial program 59.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf 53.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.2%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   4. Simplified 53.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-296}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-194}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 9: 56.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* b (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -2.9e+108)
     t_3
     (if (<= a -8e-67)
       t_2
       (if (<= a -9e-196)
         t_1
         (if (<= a -3.8e-238)
           (* t (- (* b i) (* x a)))
           (if (<= a 1.2e+61)
             t_1
             (if (<= a 3.9e+107)
               t_2
               (if (<= a 3.8e+119) (* b (- (* t i) (* z c))) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.9e+108) {
		tmp = t_3;
	} else if (a <= -8e-67) {
		tmp = t_2;
	} else if (a <= -9e-196) {
		tmp = t_1;
	} else if (a <= -3.8e-238) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 1.2e+61) {
		tmp = t_1;
	} else if (a <= 3.9e+107) {
		tmp = t_2;
	} else if (a <= 3.8e+119) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (b * (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-2.9d+108)) then
        tmp = t_3
    else if (a <= (-8d-67)) then
        tmp = t_2
    else if (a <= (-9d-196)) then
        tmp = t_1
    else if (a <= (-3.8d-238)) then
        tmp = t * ((b * i) - (x * a))
    else if (a <= 1.2d+61) then
        tmp = t_1
    else if (a <= 3.9d+107) then
        tmp = t_2
    else if (a <= 3.8d+119) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.9e+108) {
		tmp = t_3;
	} else if (a <= -8e-67) {
		tmp = t_2;
	} else if (a <= -9e-196) {
		tmp = t_1;
	} else if (a <= -3.8e-238) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 1.2e+61) {
		tmp = t_1;
	} else if (a <= 3.9e+107) {
		tmp = t_2;
	} else if (a <= 3.8e+119) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (b * (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.9e+108:
		tmp = t_3
	elif a <= -8e-67:
		tmp = t_2
	elif a <= -9e-196:
		tmp = t_1
	elif a <= -3.8e-238:
		tmp = t * ((b * i) - (x * a))
	elif a <= 1.2e+61:
		tmp = t_1
	elif a <= 3.9e+107:
		tmp = t_2
	elif a <= 3.8e+119:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.9e+108)
		tmp = t_3;
	elseif (a <= -8e-67)
		tmp = t_2;
	elseif (a <= -9e-196)
		tmp = t_1;
	elseif (a <= -3.8e-238)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (a <= 1.2e+61)
		tmp = t_1;
	elseif (a <= 3.9e+107)
		tmp = t_2;
	elseif (a <= 3.8e+119)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (b * (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.9e+108)
		tmp = t_3;
	elseif (a <= -8e-67)
		tmp = t_2;
	elseif (a <= -9e-196)
		tmp = t_1;
	elseif (a <= -3.8e-238)
		tmp = t * ((b * i) - (x * a));
	elseif (a <= 1.2e+61)
		tmp = t_1;
	elseif (a <= 3.9e+107)
		tmp = t_2;
	elseif (a <= 3.8e+119)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+108], t$95$3, If[LessEqual[a, -8e-67], t$95$2, If[LessEqual[a, -9e-196], t$95$1, If[LessEqual[a, -3.8e-238], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+61], t$95$1, If[LessEqual[a, 3.9e+107], t$95$2, If[LessEqual[a, 3.8e+119], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.90000000000000007e108 or 3.7999999999999999e119 < a

   1. Initial program 49.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 72.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 72.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 72.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 72.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 72.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -2.90000000000000007e108 < a < -7.99999999999999954e-67 or 1.1999999999999999e61 < a < 3.8999999999999998e107

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 75.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 75.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 75.8%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 75.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   if -7.99999999999999954e-67 < a < -9e-196 or -3.7999999999999997e-238 < a < 1.1999999999999999e61

   1. Initial program 78.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in i around -inf 81.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   3. Taylor expanded in y around inf 70.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z\right) \]
   4. Step-by-step derivation

      1. neg-mul-1 70.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(-i \cdot j\right)} + x \cdot z\right) - b \cdot \left(c \cdot z\right) \]

      2. +-commutative 70.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + \left(-i \cdot j\right)\right)} - b \cdot \left(c \cdot z\right) \]

      3. sub-neg 70.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z\right) \]

   if -9e-196 < a < -3.7999999999999997e-238

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. prod-diff 82.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(\mathsf{fma}\left(y, z, -a \cdot t\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 82.2%

         \[\leadsto \left(x \cdot \left(\mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. fma-neg 82.2%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. distribute-rgt-in 73.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z - t \cdot a\right) \cdot x + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.1%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative 73.1%

         \[\leadsto \left(\left(x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. fma-neg 73.1%

         \[\leadsto \left(\left(x \cdot \color{blue}{\mathsf{fma}\left(z, y, -t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. distribute-rgt-neg-in 73.1%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, \color{blue}{t \cdot \left(-a\right)}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. *-commutative 73.1%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, \color{blue}{t \cdot a}\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 73.1%

      \[\leadsto \left(\color{blue}{\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in x around 0 73.1%

      \[\leadsto \left(\left(\color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in t around inf 82.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + x \cdot \left(a + -1 \cdot a\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 82.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(a + -1 \cdot a\right) + -1 \cdot \left(a \cdot x\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. *-commutative 82.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(a + -1 \cdot a\right) \cdot x} + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      3. distribute-rgt1-in 82.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(\left(-1 + 1\right) \cdot a\right)} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      4. metadata-eval 82.7%

         \[\leadsto t \cdot \left(\left(\left(\color{blue}{0} \cdot a\right) \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      5. mul0-lft 82.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{0} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. associate-*r* 82.7%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-1 \cdot a\right) \cdot x}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. neg-mul-1 82.7%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-a\right)} \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      8. distribute-rgt-out 82.7%

         \[\leadsto t \cdot \left(\color{blue}{x \cdot \left(0 + \left(-a\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. sub-neg 82.7%

         \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(0 - a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      10. neg-sub0 82.7%

          \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(-a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      11. distribute-rgt-neg-in 82.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(-x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      12. neg-sub0 82.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(0 - x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      13. neg-mul-1 82.7%

          \[\leadsto t \cdot \left(\left(0 - x \cdot a\right) - \color{blue}{\left(-b \cdot i\right)}\right) \]

      14. associate--r+ 82.7%

          \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a + \left(-b \cdot i\right)\right)\right)} \]

      15. +-commutative 82.7%

          \[\leadsto t \cdot \left(0 - \color{blue}{\left(\left(-b \cdot i\right) + x \cdot a\right)}\right) \]

      16. associate--r+ 82.7%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - \left(-b \cdot i\right)\right) - x \cdot a\right)} \]

      17. neg-sub0 82.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(-\left(-b \cdot i\right)\right)} - x \cdot a\right) \]

      18. remove-double-neg 82.7%

          \[\leadsto t \cdot \left(\color{blue}{b \cdot i} - x \cdot a\right) \]

      19. *-commutative 82.7%

          \[\leadsto t \cdot \left(\color{blue}{i \cdot b} - x \cdot a\right) \]

   7. Simplified 82.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 3.8999999999999998e107 < a < 3.7999999999999999e119

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 10: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.05 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+152}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.05e+119)
     t_1
     (if (<= b 2.45e-30)
       (- (* x (- (* y z) (* t a))) (* j (- (* y i) (* a c))))
       (if (<= b 7.2e+152)
         (+ (* z (- (* x y) (* b c))) (* i (- (* t b) (* y j))))
         (if (<= b 8.6e+171) (* c (- (* a j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.05e+119) {
		tmp = t_1;
	} else if (b <= 2.45e-30) {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)));
	} else if (b <= 7.2e+152) {
		tmp = (z * ((x * y) - (b * c))) + (i * ((t * b) - (y * j)));
	} else if (b <= 8.6e+171) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-3.05d+119)) then
        tmp = t_1
    else if (b <= 2.45d-30) then
        tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)))
    else if (b <= 7.2d+152) then
        tmp = (z * ((x * y) - (b * c))) + (i * ((t * b) - (y * j)))
    else if (b <= 8.6d+171) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.05e+119) {
		tmp = t_1;
	} else if (b <= 2.45e-30) {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)));
	} else if (b <= 7.2e+152) {
		tmp = (z * ((x * y) - (b * c))) + (i * ((t * b) - (y * j)));
	} else if (b <= 8.6e+171) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.05e+119:
		tmp = t_1
	elif b <= 2.45e-30:
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)))
	elif b <= 7.2e+152:
		tmp = (z * ((x * y) - (b * c))) + (i * ((t * b) - (y * j)))
	elif b <= 8.6e+171:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.05e+119)
		tmp = t_1;
	elseif (b <= 2.45e-30)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (b <= 7.2e+152)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(i * Float64(Float64(t * b) - Float64(y * j))));
	elseif (b <= 8.6e+171)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.05e+119)
		tmp = t_1;
	elseif (b <= 2.45e-30)
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)));
	elseif (b <= 7.2e+152)
		tmp = (z * ((x * y) - (b * c))) + (i * ((t * b) - (y * j)));
	elseif (b <= 8.6e+171)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.05e+119], t$95$1, If[LessEqual[b, 2.45e-30], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e+152], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+171], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.05e119 or 8.60000000000000016e171 < b

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 82.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -3.05e119 < b < 2.44999999999999985e-30

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0 75.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if 2.44999999999999985e-30 < b < 7.1999999999999998e152

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in i around -inf 72.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   3. Taylor expanded in a around 0 69.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + x \cdot \left(y \cdot z\right)\right)} - b \cdot \left(c \cdot z\right) \]

   4. Taylor expanded in z around 0 75.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Taylor expanded in x around 0 69.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + x \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.4%

         \[\leadsto -1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto -1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + \left(x \cdot \color{blue}{\left(z \cdot y\right)} + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)\right) \]

      3. associate-+r+ 69.4%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + x \cdot \left(z \cdot y\right)\right) + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      4. *-commutative 69.4%

         \[\leadsto \left(-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + x \cdot \color{blue}{\left(y \cdot z\right)}\right) + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      5. +-commutative 69.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z\right) + -1 \cdot \left(b \cdot \left(c \cdot z\right)\right)\right)} + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      6. associate-*r* 75.4%

         \[\leadsto \left(\color{blue}{\left(x \cdot y\right) \cdot z} + -1 \cdot \left(b \cdot \left(c \cdot z\right)\right)\right) + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      7. mul-1-neg 75.4%

         \[\leadsto \left(\left(x \cdot y\right) \cdot z + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)}\right) + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      8. associate-*r* 72.4%

         \[\leadsto \left(\left(x \cdot y\right) \cdot z + \left(-\color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      9. distribute-lft-neg-in 72.4%

         \[\leadsto \left(\left(x \cdot y\right) \cdot z + \color{blue}{\left(-b \cdot c\right) \cdot z}\right) + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      10. distribute-rgt-in 75.4%

          \[\leadsto \color{blue}{z \cdot \left(x \cdot y + \left(-b \cdot c\right)\right)} + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      11. sub-neg 75.4%

          \[\leadsto z \cdot \color{blue}{\left(x \cdot y - b \cdot c\right)} + -1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) \]

      12. mul-1-neg 75.4%

          \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-i \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      13. *-commutative 75.4%

          \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + \left(-\color{blue}{\left(j \cdot y - b \cdot t\right) \cdot i}\right) \]

      14. distribute-rgt-neg-in 75.4%

          \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(j \cdot y - b \cdot t\right) \cdot \left(-i\right)} \]

   7. Simplified 75.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + \left(y \cdot j - b \cdot t\right) \cdot \left(-i\right)} \]

   if 7.1999999999999998e152 < b < 8.60000000000000016e171

   1. Initial program 40.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in c around inf 79.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   4. Simplified 79.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.05 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+152}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 11: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-291}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -6.5e+60)
     t_2
     (if (<= z -2.3e-21)
       t_1
       (if (<= z 9.6e-291)
         (* i (- (* t b) (* y j)))
         (if (<= z 2e-35)
           (* t (- (* b i) (* x a)))
           (if (<= z 5.7e+16)
             (* j (- (* a c) (* y i)))
             (if (<= z 3.2e+89)
               (* x (- (* y z) (* t a)))
               (if (<= z 5.1e+113) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -6.5e+60) {
		tmp = t_2;
	} else if (z <= -2.3e-21) {
		tmp = t_1;
	} else if (z <= 9.6e-291) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 2e-35) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 5.7e+16) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 3.2e+89) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= 5.1e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-6.5d+60)) then
        tmp = t_2
    else if (z <= (-2.3d-21)) then
        tmp = t_1
    else if (z <= 9.6d-291) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 2d-35) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 5.7d+16) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 3.2d+89) then
        tmp = x * ((y * z) - (t * a))
    else if (z <= 5.1d+113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -6.5e+60) {
		tmp = t_2;
	} else if (z <= -2.3e-21) {
		tmp = t_1;
	} else if (z <= 9.6e-291) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 2e-35) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 5.7e+16) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 3.2e+89) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= 5.1e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -6.5e+60:
		tmp = t_2
	elif z <= -2.3e-21:
		tmp = t_1
	elif z <= 9.6e-291:
		tmp = i * ((t * b) - (y * j))
	elif z <= 2e-35:
		tmp = t * ((b * i) - (x * a))
	elif z <= 5.7e+16:
		tmp = j * ((a * c) - (y * i))
	elif z <= 3.2e+89:
		tmp = x * ((y * z) - (t * a))
	elif z <= 5.1e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -6.5e+60)
		tmp = t_2;
	elseif (z <= -2.3e-21)
		tmp = t_1;
	elseif (z <= 9.6e-291)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 2e-35)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 5.7e+16)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 3.2e+89)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (z <= 5.1e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -6.5e+60)
		tmp = t_2;
	elseif (z <= -2.3e-21)
		tmp = t_1;
	elseif (z <= 9.6e-291)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 2e-35)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 5.7e+16)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 3.2e+89)
		tmp = x * ((y * z) - (t * a));
	elseif (z <= 5.1e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+60], t$95$2, If[LessEqual[z, -2.3e-21], t$95$1, If[LessEqual[z, 9.6e-291], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-35], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e+16], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+89], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+113], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6.49999999999999931e60 or 5.09999999999999994e113 < z

   1. Initial program 65.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in z around inf 70.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   3. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   4. Simplified 70.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -6.49999999999999931e60 < z < -2.29999999999999999e-21 or 3.19999999999999987e89 < z < 5.09999999999999994e113

   1. Initial program 44.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 67.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 67.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 67.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 67.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 67.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -2.29999999999999999e-21 < z < 9.60000000000000049e-291

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in i around -inf 81.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   3. Taylor expanded in a around 0 68.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + x \cdot \left(y \cdot z\right)\right)} - b \cdot \left(c \cdot z\right) \]

   4. Taylor expanded in z around 0 61.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Taylor expanded in i around inf 59.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 59.4%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y - b \cdot t\right)} \]

      2. *-commutative 59.4%

         \[\leadsto -\color{blue}{\left(j \cdot y - b \cdot t\right) \cdot i} \]

      3. distribute-rgt-neg-in 59.4%

         \[\leadsto \color{blue}{\left(j \cdot y - b \cdot t\right) \cdot \left(-i\right)} \]

      4. *-commutative 59.4%

         \[\leadsto \left(\color{blue}{y \cdot j} - b \cdot t\right) \cdot \left(-i\right) \]

   7. Simplified 59.4%

      \[\leadsto \color{blue}{\left(y \cdot j - b \cdot t\right) \cdot \left(-i\right)} \]

   if 9.60000000000000049e-291 < z < 2.00000000000000002e-35

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. prod-diff 69.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\mathsf{fma}\left(y, z, -a \cdot t\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 69.8%

         \[\leadsto \left(x \cdot \left(\mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. fma-neg 69.8%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. distribute-rgt-in 67.9%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z - t \cdot a\right) \cdot x + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 67.9%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative 67.9%

         \[\leadsto \left(\left(x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. fma-neg 67.9%

         \[\leadsto \left(\left(x \cdot \color{blue}{\mathsf{fma}\left(z, y, -t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. distribute-rgt-neg-in 67.9%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, \color{blue}{t \cdot \left(-a\right)}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. *-commutative 67.9%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, \color{blue}{t \cdot a}\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 67.9%

      \[\leadsto \left(\color{blue}{\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in x around 0 67.9%

      \[\leadsto \left(\left(\color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in t around inf 62.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + x \cdot \left(a + -1 \cdot a\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 62.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(a + -1 \cdot a\right) + -1 \cdot \left(a \cdot x\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. *-commutative 62.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(a + -1 \cdot a\right) \cdot x} + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      3. distribute-rgt1-in 62.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(\left(-1 + 1\right) \cdot a\right)} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      4. metadata-eval 62.7%

         \[\leadsto t \cdot \left(\left(\left(\color{blue}{0} \cdot a\right) \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      5. mul0-lft 62.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{0} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. associate-*r* 62.7%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-1 \cdot a\right) \cdot x}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. neg-mul-1 62.7%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-a\right)} \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      8. distribute-rgt-out 62.7%

         \[\leadsto t \cdot \left(\color{blue}{x \cdot \left(0 + \left(-a\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. sub-neg 62.7%

         \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(0 - a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      10. neg-sub0 62.7%

          \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(-a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      11. distribute-rgt-neg-in 62.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(-x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      12. neg-sub0 62.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(0 - x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      13. neg-mul-1 62.7%

          \[\leadsto t \cdot \left(\left(0 - x \cdot a\right) - \color{blue}{\left(-b \cdot i\right)}\right) \]

      14. associate--r+ 62.7%

          \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a + \left(-b \cdot i\right)\right)\right)} \]

      15. +-commutative 62.7%

          \[\leadsto t \cdot \left(0 - \color{blue}{\left(\left(-b \cdot i\right) + x \cdot a\right)}\right) \]

      16. associate--r+ 62.7%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - \left(-b \cdot i\right)\right) - x \cdot a\right)} \]

      17. neg-sub0 62.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(-\left(-b \cdot i\right)\right)} - x \cdot a\right) \]

      18. remove-double-neg 62.7%

          \[\leadsto t \cdot \left(\color{blue}{b \cdot i} - x \cdot a\right) \]

      19. *-commutative 62.7%

          \[\leadsto t \cdot \left(\color{blue}{i \cdot b} - x \cdot a\right) \]

   7. Simplified 62.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 2.00000000000000002e-35 < z < 5.7e16

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf 71.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 71.5%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) \]

   4. Simplified 71.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

   if 5.7e16 < z < 3.19999999999999987e89

   1. Initial program 60.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 86.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 86.9%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 86.9%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 86.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-291}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 12: 66.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+120} \lor \neg \left(b \leq 2.3 \cdot 10^{+172}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.8e+120) (not (<= b 2.3e+172)))
   (* b (- (* t i) (* z c)))
   (- (* x (- (* y z) (* t a))) (* j (- (* y i) (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.8e+120) || !(b <= 2.3e+172)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.8d+120)) .or. (.not. (b <= 2.3d+172))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.8e+120) || !(b <= 2.3e+172)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.8e+120) or not (b <= 2.3e+172):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.8e+120) || !(b <= 2.3e+172))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.8e+120) || ~((b <= 2.3e+172)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.8e+120], N[Not[LessEqual[b, 2.3e+172]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.7999999999999998e120 or 2.3000000000000001e172 < b

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 82.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -3.7999999999999998e120 < b < 2.3000000000000001e172

   1. Initial program 68.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around 0 72.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+120} \lor \neg \left(b \leq 2.3 \cdot 10^{+172}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 13: 42.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -4.1e-199)
     t_2
     (if (<= a -4.6e-299)
       (* y (* x z))
       (if (<= a 3.2e-284)
         (* i (* j (- y)))
         (if (<= a 1.5e-130)
           t_1
           (if (<= a 2.6e-89)
             (* b (* z (- c)))
             (if (<= a 1.4e+18) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.1e-199) {
		tmp = t_2;
	} else if (a <= -4.6e-299) {
		tmp = y * (x * z);
	} else if (a <= 3.2e-284) {
		tmp = i * (j * -y);
	} else if (a <= 1.5e-130) {
		tmp = t_1;
	} else if (a <= 2.6e-89) {
		tmp = b * (z * -c);
	} else if (a <= 1.4e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-4.1d-199)) then
        tmp = t_2
    else if (a <= (-4.6d-299)) then
        tmp = y * (x * z)
    else if (a <= 3.2d-284) then
        tmp = i * (j * -y)
    else if (a <= 1.5d-130) then
        tmp = t_1
    else if (a <= 2.6d-89) then
        tmp = b * (z * -c)
    else if (a <= 1.4d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.1e-199) {
		tmp = t_2;
	} else if (a <= -4.6e-299) {
		tmp = y * (x * z);
	} else if (a <= 3.2e-284) {
		tmp = i * (j * -y);
	} else if (a <= 1.5e-130) {
		tmp = t_1;
	} else if (a <= 2.6e-89) {
		tmp = b * (z * -c);
	} else if (a <= 1.4e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.1e-199:
		tmp = t_2
	elif a <= -4.6e-299:
		tmp = y * (x * z)
	elif a <= 3.2e-284:
		tmp = i * (j * -y)
	elif a <= 1.5e-130:
		tmp = t_1
	elif a <= 2.6e-89:
		tmp = b * (z * -c)
	elif a <= 1.4e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.1e-199)
		tmp = t_2;
	elseif (a <= -4.6e-299)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 3.2e-284)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (a <= 1.5e-130)
		tmp = t_1;
	elseif (a <= 2.6e-89)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 1.4e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.1e-199)
		tmp = t_2;
	elseif (a <= -4.6e-299)
		tmp = y * (x * z);
	elseif (a <= 3.2e-284)
		tmp = i * (j * -y);
	elseif (a <= 1.5e-130)
		tmp = t_1;
	elseif (a <= 2.6e-89)
		tmp = b * (z * -c);
	elseif (a <= 1.4e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e-199], t$95$2, If[LessEqual[a, -4.6e-299], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-284], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-130], t$95$1, If[LessEqual[a, 2.6e-89], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+18], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.10000000000000022e-199 or 1.4e18 < a

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 56.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 56.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 56.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -4.10000000000000022e-199 < a < -4.6000000000000001e-299

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 63.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 63.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 63.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 63.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 63.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 63.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around inf 53.2%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -4.6000000000000001e-299 < a < 3.20000000000000024e-284

   1. Initial program 55.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 72.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 72.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 72.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 72.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 72.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 72.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around 0 63.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.8%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 63.8%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if 3.20000000000000024e-284 < a < 1.49999999999999993e-130 or 2.5999999999999999e-89 < a < 1.4e18

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 51.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.1%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 51.1%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 51.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 47.1%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 47.1%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 1.49999999999999993e-130 < a < 2.5999999999999999e-89

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 100.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in z around inf 60.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.7%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 60.7%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 60.7%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 14: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+222}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-285}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= a -3.9e+222)
     (* a (* c j))
     (if (<= a -1.5e-10)
       (* t (* x (- a)))
       (if (<= a -3.2e-298)
         t_1
         (if (<= a 8e-285)
           (* i (* j (- y)))
           (if (<= a 4.5e-131)
             (* x (* y z))
             (if (<= a 1.2e-88)
               (* b (* z (- c)))
               (if (<= a 1.65e+99) t_1 (* x (* t (- a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (a <= -3.9e+222) {
		tmp = a * (c * j);
	} else if (a <= -1.5e-10) {
		tmp = t * (x * -a);
	} else if (a <= -3.2e-298) {
		tmp = t_1;
	} else if (a <= 8e-285) {
		tmp = i * (j * -y);
	} else if (a <= 4.5e-131) {
		tmp = x * (y * z);
	} else if (a <= 1.2e-88) {
		tmp = b * (z * -c);
	} else if (a <= 1.65e+99) {
		tmp = t_1;
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (a <= (-3.9d+222)) then
        tmp = a * (c * j)
    else if (a <= (-1.5d-10)) then
        tmp = t * (x * -a)
    else if (a <= (-3.2d-298)) then
        tmp = t_1
    else if (a <= 8d-285) then
        tmp = i * (j * -y)
    else if (a <= 4.5d-131) then
        tmp = x * (y * z)
    else if (a <= 1.2d-88) then
        tmp = b * (z * -c)
    else if (a <= 1.65d+99) then
        tmp = t_1
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (a <= -3.9e+222) {
		tmp = a * (c * j);
	} else if (a <= -1.5e-10) {
		tmp = t * (x * -a);
	} else if (a <= -3.2e-298) {
		tmp = t_1;
	} else if (a <= 8e-285) {
		tmp = i * (j * -y);
	} else if (a <= 4.5e-131) {
		tmp = x * (y * z);
	} else if (a <= 1.2e-88) {
		tmp = b * (z * -c);
	} else if (a <= 1.65e+99) {
		tmp = t_1;
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if a <= -3.9e+222:
		tmp = a * (c * j)
	elif a <= -1.5e-10:
		tmp = t * (x * -a)
	elif a <= -3.2e-298:
		tmp = t_1
	elif a <= 8e-285:
		tmp = i * (j * -y)
	elif a <= 4.5e-131:
		tmp = x * (y * z)
	elif a <= 1.2e-88:
		tmp = b * (z * -c)
	elif a <= 1.65e+99:
		tmp = t_1
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (a <= -3.9e+222)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -1.5e-10)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -3.2e-298)
		tmp = t_1;
	elseif (a <= 8e-285)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (a <= 4.5e-131)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1.2e-88)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 1.65e+99)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (a <= -3.9e+222)
		tmp = a * (c * j);
	elseif (a <= -1.5e-10)
		tmp = t * (x * -a);
	elseif (a <= -3.2e-298)
		tmp = t_1;
	elseif (a <= 8e-285)
		tmp = i * (j * -y);
	elseif (a <= 4.5e-131)
		tmp = x * (y * z);
	elseif (a <= 1.2e-88)
		tmp = b * (z * -c);
	elseif (a <= 1.65e+99)
		tmp = t_1;
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+222], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-10], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.2e-298], t$95$1, If[LessEqual[a, 8e-285], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-131], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-88], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+99], t$95$1, N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -3.8999999999999999e222

   1. Initial program 36.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 76.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 76.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 76.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 76.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 76.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 76.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -3.8999999999999999e222 < a < -1.5e-10

   1. Initial program 63.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in t around inf 63.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. distribute-lft-out-- 63.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

   4. Simplified 63.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

   5. Taylor expanded in a around inf 51.8%

      \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -1.5e-10 < a < -3.19999999999999997e-298 or 1.2e-88 < a < 1.65e99

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 51.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 51.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 51.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around inf 37.4%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -3.19999999999999997e-298 < a < 8.00000000000000059e-285

   1. Initial program 55.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 72.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 72.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 72.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 72.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 72.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 72.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around 0 63.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.8%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 63.8%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if 8.00000000000000059e-285 < a < 4.5000000000000002e-131

   1. Initial program 90.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 52.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 52.0%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 52.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 48.3%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 48.3%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 4.5000000000000002e-131 < a < 1.2e-88

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 100.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in z around inf 60.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.7%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 60.7%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 60.7%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]

   if 1.65e99 < a

   1. Initial program 55.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 51.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 51.6%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 51.6%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around 0 48.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. *-commutative 48.9%

         \[\leadsto x \cdot \left(-\color{blue}{t \cdot a}\right) \]

      3. distribute-rgt-neg-in 48.9%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   7. Simplified 48.9%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+222}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-298}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-285}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 15: 50.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.9e+107)
     t_1
     (if (<= a -7e-85)
       (* x (- (* y z) (* t a)))
       (if (<= a -2.4e-191)
         (* j (- (* a c) (* y i)))
         (if (<= a -2.5e-238)
           (* t (- (* b i) (* x a)))
           (if (<= a 2.55e+40) (* y (- (* x z) (* i j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.9e+107) {
		tmp = t_1;
	} else if (a <= -7e-85) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -2.4e-191) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= -2.5e-238) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 2.55e+40) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-2.9d+107)) then
        tmp = t_1
    else if (a <= (-7d-85)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-2.4d-191)) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= (-2.5d-238)) then
        tmp = t * ((b * i) - (x * a))
    else if (a <= 2.55d+40) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.9e+107) {
		tmp = t_1;
	} else if (a <= -7e-85) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -2.4e-191) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= -2.5e-238) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 2.55e+40) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.9e+107:
		tmp = t_1
	elif a <= -7e-85:
		tmp = x * ((y * z) - (t * a))
	elif a <= -2.4e-191:
		tmp = j * ((a * c) - (y * i))
	elif a <= -2.5e-238:
		tmp = t * ((b * i) - (x * a))
	elif a <= 2.55e+40:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.9e+107)
		tmp = t_1;
	elseif (a <= -7e-85)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -2.4e-191)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= -2.5e-238)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (a <= 2.55e+40)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.9e+107)
		tmp = t_1;
	elseif (a <= -7e-85)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -2.4e-191)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= -2.5e-238)
		tmp = t * ((b * i) - (x * a));
	elseif (a <= 2.55e+40)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+107], t$95$1, If[LessEqual[a, -7e-85], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-191], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-238], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e+40], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.89999999999999988e107 or 2.54999999999999979e40 < a

   1. Initial program 57.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 67.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 67.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 67.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 67.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -2.89999999999999988e107 < a < -6.99999999999999956e-85

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 68.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 68.2%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 68.2%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 68.2%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   if -6.99999999999999956e-85 < a < -2.3999999999999999e-191

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf 59.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 59.1%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) \]

   4. Simplified 59.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

   if -2.3999999999999999e-191 < a < -2.5e-238

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. prod-diff 82.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(\mathsf{fma}\left(y, z, -a \cdot t\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 82.2%

         \[\leadsto \left(x \cdot \left(\mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. fma-neg 82.2%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. distribute-rgt-in 73.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z - t \cdot a\right) \cdot x + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.1%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative 73.1%

         \[\leadsto \left(\left(x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. fma-neg 73.1%

         \[\leadsto \left(\left(x \cdot \color{blue}{\mathsf{fma}\left(z, y, -t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. distribute-rgt-neg-in 73.1%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, \color{blue}{t \cdot \left(-a\right)}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. *-commutative 73.1%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, \color{blue}{t \cdot a}\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 73.1%

      \[\leadsto \left(\color{blue}{\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in x around 0 73.1%

      \[\leadsto \left(\left(\color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in t around inf 82.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + x \cdot \left(a + -1 \cdot a\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 82.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(a + -1 \cdot a\right) + -1 \cdot \left(a \cdot x\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. *-commutative 82.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(a + -1 \cdot a\right) \cdot x} + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      3. distribute-rgt1-in 82.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(\left(-1 + 1\right) \cdot a\right)} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      4. metadata-eval 82.7%

         \[\leadsto t \cdot \left(\left(\left(\color{blue}{0} \cdot a\right) \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      5. mul0-lft 82.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{0} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. associate-*r* 82.7%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-1 \cdot a\right) \cdot x}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. neg-mul-1 82.7%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-a\right)} \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      8. distribute-rgt-out 82.7%

         \[\leadsto t \cdot \left(\color{blue}{x \cdot \left(0 + \left(-a\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. sub-neg 82.7%

         \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(0 - a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      10. neg-sub0 82.7%

          \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(-a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      11. distribute-rgt-neg-in 82.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(-x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      12. neg-sub0 82.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(0 - x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      13. neg-mul-1 82.7%

          \[\leadsto t \cdot \left(\left(0 - x \cdot a\right) - \color{blue}{\left(-b \cdot i\right)}\right) \]

      14. associate--r+ 82.7%

          \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a + \left(-b \cdot i\right)\right)\right)} \]

      15. +-commutative 82.7%

          \[\leadsto t \cdot \left(0 - \color{blue}{\left(\left(-b \cdot i\right) + x \cdot a\right)}\right) \]

      16. associate--r+ 82.7%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - \left(-b \cdot i\right)\right) - x \cdot a\right)} \]

      17. neg-sub0 82.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(-\left(-b \cdot i\right)\right)} - x \cdot a\right) \]

      18. remove-double-neg 82.7%

          \[\leadsto t \cdot \left(\color{blue}{b \cdot i} - x \cdot a\right) \]

      19. *-commutative 82.7%

          \[\leadsto t \cdot \left(\color{blue}{i \cdot b} - x \cdot a\right) \]

   7. Simplified 82.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -2.5e-238 < a < 2.54999999999999979e40

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 60.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 60.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 60.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 60.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 60.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 16: 29.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-246}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.5e+95)
   (* b (* t i))
   (if (<= b -1.3e-42)
     (* i (* j (- y)))
     (if (<= b -1.75e-99)
       (* a (* x (- t)))
       (if (<= b -2.6e-246)
         (* a (* c j))
         (if (<= b 1.45e-248)
           (* x (* t (- a)))
           (if (<= b 6.9e+37) (* x (* y z)) (* c (* z (- b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.5e+95) {
		tmp = b * (t * i);
	} else if (b <= -1.3e-42) {
		tmp = i * (j * -y);
	} else if (b <= -1.75e-99) {
		tmp = a * (x * -t);
	} else if (b <= -2.6e-246) {
		tmp = a * (c * j);
	} else if (b <= 1.45e-248) {
		tmp = x * (t * -a);
	} else if (b <= 6.9e+37) {
		tmp = x * (y * z);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.5d+95)) then
        tmp = b * (t * i)
    else if (b <= (-1.3d-42)) then
        tmp = i * (j * -y)
    else if (b <= (-1.75d-99)) then
        tmp = a * (x * -t)
    else if (b <= (-2.6d-246)) then
        tmp = a * (c * j)
    else if (b <= 1.45d-248) then
        tmp = x * (t * -a)
    else if (b <= 6.9d+37) then
        tmp = x * (y * z)
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.5e+95) {
		tmp = b * (t * i);
	} else if (b <= -1.3e-42) {
		tmp = i * (j * -y);
	} else if (b <= -1.75e-99) {
		tmp = a * (x * -t);
	} else if (b <= -2.6e-246) {
		tmp = a * (c * j);
	} else if (b <= 1.45e-248) {
		tmp = x * (t * -a);
	} else if (b <= 6.9e+37) {
		tmp = x * (y * z);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.5e+95:
		tmp = b * (t * i)
	elif b <= -1.3e-42:
		tmp = i * (j * -y)
	elif b <= -1.75e-99:
		tmp = a * (x * -t)
	elif b <= -2.6e-246:
		tmp = a * (c * j)
	elif b <= 1.45e-248:
		tmp = x * (t * -a)
	elif b <= 6.9e+37:
		tmp = x * (y * z)
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.5e+95)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -1.3e-42)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (b <= -1.75e-99)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (b <= -2.6e-246)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.45e-248)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (b <= 6.9e+37)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.5e+95)
		tmp = b * (t * i);
	elseif (b <= -1.3e-42)
		tmp = i * (j * -y);
	elseif (b <= -1.75e-99)
		tmp = a * (x * -t);
	elseif (b <= -2.6e-246)
		tmp = a * (c * j);
	elseif (b <= 1.45e-248)
		tmp = x * (t * -a);
	elseif (b <= 6.9e+37)
		tmp = x * (y * z);
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.5e+95], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e-42], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.75e-99], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-246], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-248], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.9e+37], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.4999999999999997e95

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 76.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 76.8%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 84.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 84.0%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 84.0%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 84.0%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 84.0%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 81.7%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 81.7%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 81.7%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 81.7%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 81.7%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 81.7%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 81.7%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 81.7%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 84.0%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 84.0%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 84.0%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 56.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -5.4999999999999997e95 < b < -1.3e-42

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 64.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 64.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 64.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around 0 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.6%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 44.6%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   7. Simplified 44.6%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if -1.3e-42 < b < -1.7499999999999999e-99

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 78.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 78.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 78.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 78.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 78.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around 0 65.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 65.4%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-rgt-neg-in 65.4%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   7. Simplified 65.4%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   if -1.7499999999999999e-99 < b < -2.5999999999999999e-246

   1. Initial program 58.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 55.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 55.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 55.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 44.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.2%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 44.2%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -2.5999999999999999e-246 < b < 1.4500000000000001e-248

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 60.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 60.4%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 60.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around 0 43.3%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. *-commutative 43.3%

         \[\leadsto x \cdot \left(-\color{blue}{t \cdot a}\right) \]

      3. distribute-rgt-neg-in 43.3%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   7. Simplified 43.3%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   if 1.4500000000000001e-248 < b < 6.8999999999999996e37

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 55.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 55.0%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 55.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 40.7%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 40.7%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 6.8999999999999996e37 < b

   1. Initial program 65.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 56.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 56.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in z around inf 40.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.5%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 40.5%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 40.5%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   7. Simplified 40.5%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-neg-out 40.5%

         \[\leadsto \color{blue}{-b \cdot \left(z \cdot c\right)} \]

      2. add-sqr-sqrt 40.4%

         \[\leadsto -\color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot \left(z \cdot c\right) \]

      3. sqrt-unprod 37.8%

         \[\leadsto -\color{blue}{\sqrt{b \cdot b}} \cdot \left(z \cdot c\right) \]

      4. sqr-neg 37.8%

         \[\leadsto -\sqrt{\color{blue}{\left(-b\right) \cdot \left(-b\right)}} \cdot \left(z \cdot c\right) \]

      5. sqrt-unprod 0.0%

         \[\leadsto -\color{blue}{\left(\sqrt{-b} \cdot \sqrt{-b}\right)} \cdot \left(z \cdot c\right) \]

      6. add-sqr-sqrt 13.2%

         \[\leadsto -\color{blue}{\left(-b\right)} \cdot \left(z \cdot c\right) \]

      7. associate-*r* 13.2%

         \[\leadsto -\color{blue}{\left(\left(-b\right) \cdot z\right) \cdot c} \]

      8. add-sqr-sqrt 0.0%

         \[\leadsto -\left(\color{blue}{\left(\sqrt{-b} \cdot \sqrt{-b}\right)} \cdot z\right) \cdot c \]

      9. sqrt-unprod 41.8%

         \[\leadsto -\left(\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}} \cdot z\right) \cdot c \]

      10. sqr-neg 41.8%

          \[\leadsto -\left(\sqrt{\color{blue}{b \cdot b}} \cdot z\right) \cdot c \]

      11. sqrt-unprod 43.5%

          \[\leadsto -\left(\color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot z\right) \cdot c \]

      12. add-sqr-sqrt 43.6%

          \[\leadsto -\left(\color{blue}{b} \cdot z\right) \cdot c \]

   9. Applied egg-rr 43.6%

      \[\leadsto \color{blue}{-\left(b \cdot z\right) \cdot c} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-246}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 17: 49.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.5e+152)
     t_1
     (if (<= j -8e-148)
       (* a (- (* c j) (* x t)))
       (if (<= j -3.2e-216)
         (* x (* y z))
         (if (<= j 2.9e+15) (* b (- (* t i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.5e+152) {
		tmp = t_1;
	} else if (j <= -8e-148) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -3.2e-216) {
		tmp = x * (y * z);
	} else if (j <= 2.9e+15) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.5d+152)) then
        tmp = t_1
    else if (j <= (-8d-148)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-3.2d-216)) then
        tmp = x * (y * z)
    else if (j <= 2.9d+15) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.5e+152) {
		tmp = t_1;
	} else if (j <= -8e-148) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -3.2e-216) {
		tmp = x * (y * z);
	} else if (j <= 2.9e+15) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.5e+152:
		tmp = t_1
	elif j <= -8e-148:
		tmp = a * ((c * j) - (x * t))
	elif j <= -3.2e-216:
		tmp = x * (y * z)
	elif j <= 2.9e+15:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.5e+152)
		tmp = t_1;
	elseif (j <= -8e-148)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -3.2e-216)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 2.9e+15)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.5e+152)
		tmp = t_1;
	elseif (j <= -8e-148)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -3.2e-216)
		tmp = x * (y * z);
	elseif (j <= 2.9e+15)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+152], t$95$1, If[LessEqual[j, -8e-148], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.2e-216], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+15], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.49999999999999995e152 or 2.9e15 < j

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf 77.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 77.7%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) \]

   4. Simplified 77.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

   if -1.49999999999999995e152 < j < -7.99999999999999949e-148

   1. Initial program 65.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 45.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -7.99999999999999949e-148 < j < -3.20000000000000026e-216

   1. Initial program 57.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 71.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 71.9%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 71.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 65.1%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 65.1%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if -3.20000000000000026e-216 < j < 2.9e15

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 47.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+152}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 18: 49.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.4 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.96 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -4.4e+173)
     t_2
     (if (<= j -6.2e-148)
       t_1
       (if (<= j -8.6e-215) (* x (* y z)) (if (<= j 1.96e-56) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -4.4e+173) {
		tmp = t_2;
	} else if (j <= -6.2e-148) {
		tmp = t_1;
	} else if (j <= -8.6e-215) {
		tmp = x * (y * z);
	} else if (j <= 1.96e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-4.4d+173)) then
        tmp = t_2
    else if (j <= (-6.2d-148)) then
        tmp = t_1
    else if (j <= (-8.6d-215)) then
        tmp = x * (y * z)
    else if (j <= 1.96d-56) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -4.4e+173) {
		tmp = t_2;
	} else if (j <= -6.2e-148) {
		tmp = t_1;
	} else if (j <= -8.6e-215) {
		tmp = x * (y * z);
	} else if (j <= 1.96e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -4.4e+173:
		tmp = t_2
	elif j <= -6.2e-148:
		tmp = t_1
	elif j <= -8.6e-215:
		tmp = x * (y * z)
	elif j <= 1.96e-56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -4.4e+173)
		tmp = t_2;
	elseif (j <= -6.2e-148)
		tmp = t_1;
	elseif (j <= -8.6e-215)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.96e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -4.4e+173)
		tmp = t_2;
	elseif (j <= -6.2e-148)
		tmp = t_1;
	elseif (j <= -8.6e-215)
		tmp = x * (y * z);
	elseif (j <= 1.96e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.4e+173], t$95$2, If[LessEqual[j, -6.2e-148], t$95$1, If[LessEqual[j, -8.6e-215], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.96e-56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.4e173 or 1.95999999999999995e-56 < j

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around inf 71.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 71.4%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) \]

   4. Simplified 71.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

   if -4.4e173 < j < -6.2000000000000003e-148 or -8.60000000000000049e-215 < j < 1.95999999999999995e-56

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. prod-diff 66.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\mathsf{fma}\left(y, z, -a \cdot t\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 66.0%

         \[\leadsto \left(x \cdot \left(\mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. fma-neg 66.0%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. distribute-rgt-in 64.6%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z - t \cdot a\right) \cdot x + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.6%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative 64.6%

         \[\leadsto \left(\left(x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. fma-neg 64.6%

         \[\leadsto \left(\left(x \cdot \color{blue}{\mathsf{fma}\left(z, y, -t \cdot a\right)} + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. distribute-rgt-neg-in 64.6%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, \color{blue}{t \cdot \left(-a\right)}\right) + \mathsf{fma}\left(-a, t, a \cdot t\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. *-commutative 64.6%

         \[\leadsto \left(\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, \color{blue}{t \cdot a}\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 64.6%

      \[\leadsto \left(\color{blue}{\left(x \cdot \mathsf{fma}\left(z, y, t \cdot \left(-a\right)\right) + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in x around 0 64.6%

      \[\leadsto \left(\left(\color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} + \mathsf{fma}\left(-a, t, t \cdot a\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in t around inf 50.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + x \cdot \left(a + -1 \cdot a\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(a + -1 \cdot a\right) + -1 \cdot \left(a \cdot x\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. *-commutative 50.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(a + -1 \cdot a\right) \cdot x} + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      3. distribute-rgt1-in 50.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(\left(-1 + 1\right) \cdot a\right)} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      4. metadata-eval 50.5%

         \[\leadsto t \cdot \left(\left(\left(\color{blue}{0} \cdot a\right) \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      5. mul0-lft 50.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{0} \cdot x + -1 \cdot \left(a \cdot x\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. associate-*r* 50.5%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-1 \cdot a\right) \cdot x}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. neg-mul-1 50.5%

         \[\leadsto t \cdot \left(\left(0 \cdot x + \color{blue}{\left(-a\right)} \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      8. distribute-rgt-out 50.5%

         \[\leadsto t \cdot \left(\color{blue}{x \cdot \left(0 + \left(-a\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. sub-neg 50.5%

         \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(0 - a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      10. neg-sub0 50.5%

          \[\leadsto t \cdot \left(x \cdot \color{blue}{\left(-a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      11. distribute-rgt-neg-in 50.5%

          \[\leadsto t \cdot \left(\color{blue}{\left(-x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      12. neg-sub0 50.5%

          \[\leadsto t \cdot \left(\color{blue}{\left(0 - x \cdot a\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      13. neg-mul-1 50.5%

          \[\leadsto t \cdot \left(\left(0 - x \cdot a\right) - \color{blue}{\left(-b \cdot i\right)}\right) \]

      14. associate--r+ 50.5%

          \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a + \left(-b \cdot i\right)\right)\right)} \]

      15. +-commutative 50.5%

          \[\leadsto t \cdot \left(0 - \color{blue}{\left(\left(-b \cdot i\right) + x \cdot a\right)}\right) \]

      16. associate--r+ 50.5%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - \left(-b \cdot i\right)\right) - x \cdot a\right)} \]

      17. neg-sub0 50.5%

          \[\leadsto t \cdot \left(\color{blue}{\left(-\left(-b \cdot i\right)\right)} - x \cdot a\right) \]

      18. remove-double-neg 50.5%

          \[\leadsto t \cdot \left(\color{blue}{b \cdot i} - x \cdot a\right) \]

      19. *-commutative 50.5%

          \[\leadsto t \cdot \left(\color{blue}{i \cdot b} - x \cdot a\right) \]

   7. Simplified 50.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -6.2000000000000003e-148 < j < -8.60000000000000049e-215

   1. Initial program 54.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 69.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 69.9%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 69.9%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 69.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 69.7%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 69.7%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 69.7%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.4 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.96 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 19: 28.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -6.3 \cdot 10^{+221}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= a -6.3e+221)
     (* a (* c j))
     (if (<= a -6.2e-12)
       t_1
       (if (<= a -2.2e-191)
         (* j (* a c))
         (if (<= a -3.8e-242)
           (* t (* b i))
           (if (<= a 9.6e+98) (* y (* x z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (a <= -6.3e+221) {
		tmp = a * (c * j);
	} else if (a <= -6.2e-12) {
		tmp = t_1;
	} else if (a <= -2.2e-191) {
		tmp = j * (a * c);
	} else if (a <= -3.8e-242) {
		tmp = t * (b * i);
	} else if (a <= 9.6e+98) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (a <= (-6.3d+221)) then
        tmp = a * (c * j)
    else if (a <= (-6.2d-12)) then
        tmp = t_1
    else if (a <= (-2.2d-191)) then
        tmp = j * (a * c)
    else if (a <= (-3.8d-242)) then
        tmp = t * (b * i)
    else if (a <= 9.6d+98) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (a <= -6.3e+221) {
		tmp = a * (c * j);
	} else if (a <= -6.2e-12) {
		tmp = t_1;
	} else if (a <= -2.2e-191) {
		tmp = j * (a * c);
	} else if (a <= -3.8e-242) {
		tmp = t * (b * i);
	} else if (a <= 9.6e+98) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if a <= -6.3e+221:
		tmp = a * (c * j)
	elif a <= -6.2e-12:
		tmp = t_1
	elif a <= -2.2e-191:
		tmp = j * (a * c)
	elif a <= -3.8e-242:
		tmp = t * (b * i)
	elif a <= 9.6e+98:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (a <= -6.3e+221)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -6.2e-12)
		tmp = t_1;
	elseif (a <= -2.2e-191)
		tmp = Float64(j * Float64(a * c));
	elseif (a <= -3.8e-242)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 9.6e+98)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	tmp = 0.0;
	if (a <= -6.3e+221)
		tmp = a * (c * j);
	elseif (a <= -6.2e-12)
		tmp = t_1;
	elseif (a <= -2.2e-191)
		tmp = j * (a * c);
	elseif (a <= -3.8e-242)
		tmp = t * (b * i);
	elseif (a <= 9.6e+98)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.3e+221], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-12], t$95$1, If[LessEqual[a, -2.2e-191], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-242], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e+98], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.2999999999999997e221

   1. Initial program 36.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 76.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 76.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 76.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 76.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 76.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 76.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -6.2999999999999997e221 < a < -6.2000000000000002e-12 or 9.5999999999999995e98 < a

   1. Initial program 59.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 63.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 63.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 63.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 63.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 63.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around 0 43.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 43.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-rgt-neg-in 43.6%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   7. Simplified 43.6%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   if -6.2000000000000002e-12 < a < -2.19999999999999998e-191

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 24.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 24.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 24.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 24.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 24.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 17.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 17.7%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 17.7%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Taylor expanded in a around 0 17.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 17.7%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. *-commutative 17.7%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot a \]

      3. associate-*l* 24.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

      4. *-commutative 24.4%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   10. Simplified 24.4%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if -2.19999999999999998e-191 < a < -3.8000000000000002e-242

   1. Initial program 83.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 64.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 64.5%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 64.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 51.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 51.7%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 51.7%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 51.7%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 51.7%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 51.7%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 51.7%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 51.7%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 51.7%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 51.7%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 51.7%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 51.7%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 51.7%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 51.7%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 51.7%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 51.7%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 51.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 52.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 52.2%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 52.2%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*l* 60.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   10. Simplified 60.3%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -3.8000000000000002e-242 < a < 9.5999999999999995e98

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 58.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 58.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 58.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 58.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 58.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around inf 39.2%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{+221}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 20: 28.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+226}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.3e+226)
   (* a (* c j))
   (if (<= a -1.25e-9)
     (* a (* x (- t)))
     (if (<= a -4.2e-191)
       (* j (* a c))
       (if (<= a -2.95e-241)
         (* t (* b i))
         (if (<= a 8.4e+93) (* y (* x z)) (* x (* t (- a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.3e+226) {
		tmp = a * (c * j);
	} else if (a <= -1.25e-9) {
		tmp = a * (x * -t);
	} else if (a <= -4.2e-191) {
		tmp = j * (a * c);
	} else if (a <= -2.95e-241) {
		tmp = t * (b * i);
	} else if (a <= 8.4e+93) {
		tmp = y * (x * z);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.3d+226)) then
        tmp = a * (c * j)
    else if (a <= (-1.25d-9)) then
        tmp = a * (x * -t)
    else if (a <= (-4.2d-191)) then
        tmp = j * (a * c)
    else if (a <= (-2.95d-241)) then
        tmp = t * (b * i)
    else if (a <= 8.4d+93) then
        tmp = y * (x * z)
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.3e+226) {
		tmp = a * (c * j);
	} else if (a <= -1.25e-9) {
		tmp = a * (x * -t);
	} else if (a <= -4.2e-191) {
		tmp = j * (a * c);
	} else if (a <= -2.95e-241) {
		tmp = t * (b * i);
	} else if (a <= 8.4e+93) {
		tmp = y * (x * z);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.3e+226:
		tmp = a * (c * j)
	elif a <= -1.25e-9:
		tmp = a * (x * -t)
	elif a <= -4.2e-191:
		tmp = j * (a * c)
	elif a <= -2.95e-241:
		tmp = t * (b * i)
	elif a <= 8.4e+93:
		tmp = y * (x * z)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.3e+226)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -1.25e-9)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (a <= -4.2e-191)
		tmp = Float64(j * Float64(a * c));
	elseif (a <= -2.95e-241)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 8.4e+93)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.3e+226)
		tmp = a * (c * j);
	elseif (a <= -1.25e-9)
		tmp = a * (x * -t);
	elseif (a <= -4.2e-191)
		tmp = j * (a * c);
	elseif (a <= -2.95e-241)
		tmp = t * (b * i);
	elseif (a <= 8.4e+93)
		tmp = y * (x * z);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.3e+226], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-9], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-191], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.95e-241], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e+93], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.3000000000000001e226

   1. Initial program 36.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 76.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 76.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 76.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 76.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 76.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 76.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -1.3000000000000001e226 < a < -1.25e-9

   1. Initial program 63.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 58.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 58.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around 0 43.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 43.4%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-rgt-neg-in 43.4%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   7. Simplified 43.4%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   if -1.25e-9 < a < -4.19999999999999971e-191

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 24.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 24.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 24.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 24.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 24.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 17.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 17.7%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 17.7%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Taylor expanded in a around 0 17.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 17.7%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. *-commutative 17.7%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot a \]

      3. associate-*l* 24.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

      4. *-commutative 24.4%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   10. Simplified 24.4%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if -4.19999999999999971e-191 < a < -2.9499999999999999e-241

   1. Initial program 83.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 64.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 64.5%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 64.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 51.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 51.7%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 51.7%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 51.7%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 51.7%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 51.7%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 51.7%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 51.7%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 51.7%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 51.7%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 51.7%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 51.7%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 51.7%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 51.7%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 51.7%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 51.7%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 51.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 52.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 52.2%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 52.2%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*l* 60.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   10. Simplified 60.3%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -2.9499999999999999e-241 < a < 8.39999999999999921e93

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 58.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 58.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 58.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 58.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 58.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around inf 39.2%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if 8.39999999999999921e93 < a

   1. Initial program 55.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 51.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 51.6%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 51.6%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around 0 48.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. *-commutative 48.9%

         \[\leadsto x \cdot \left(-\color{blue}{t \cdot a}\right) \]

      3. distribute-rgt-neg-in 48.9%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   7. Simplified 48.9%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+226}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 21: 30.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+235}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.7e+84)
   (* a (* c j))
   (if (<= j -7.5e-55)
     (* x (* t (- a)))
     (if (<= j 5e+47)
       (* x (* y z))
       (if (<= j 8e+235) (* y (* j (- i))) (* j (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.7e+84) {
		tmp = a * (c * j);
	} else if (j <= -7.5e-55) {
		tmp = x * (t * -a);
	} else if (j <= 5e+47) {
		tmp = x * (y * z);
	} else if (j <= 8e+235) {
		tmp = y * (j * -i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.7d+84)) then
        tmp = a * (c * j)
    else if (j <= (-7.5d-55)) then
        tmp = x * (t * -a)
    else if (j <= 5d+47) then
        tmp = x * (y * z)
    else if (j <= 8d+235) then
        tmp = y * (j * -i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.7e+84) {
		tmp = a * (c * j);
	} else if (j <= -7.5e-55) {
		tmp = x * (t * -a);
	} else if (j <= 5e+47) {
		tmp = x * (y * z);
	} else if (j <= 8e+235) {
		tmp = y * (j * -i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.7e+84:
		tmp = a * (c * j)
	elif j <= -7.5e-55:
		tmp = x * (t * -a)
	elif j <= 5e+47:
		tmp = x * (y * z)
	elif j <= 8e+235:
		tmp = y * (j * -i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.7e+84)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= -7.5e-55)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 5e+47)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 8e+235)
		tmp = Float64(y * Float64(j * Float64(-i)));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.7e+84)
		tmp = a * (c * j);
	elseif (j <= -7.5e-55)
		tmp = x * (t * -a);
	elseif (j <= 5e+47)
		tmp = x * (y * z);
	elseif (j <= 8e+235)
		tmp = y * (j * -i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.7e+84], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e-55], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+47], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+235], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.7e84

   1. Initial program 55.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 56.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 56.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 56.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 48.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 48.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -2.7e84 < j < -7.50000000000000023e-55

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 53.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 53.0%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 53.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around 0 37.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.8%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. *-commutative 37.8%

         \[\leadsto x \cdot \left(-\color{blue}{t \cdot a}\right) \]

      3. distribute-rgt-neg-in 37.8%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   7. Simplified 37.8%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   if -7.50000000000000023e-55 < j < 5.00000000000000022e47

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 52.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 52.5%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 52.5%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 33.8%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.8%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 33.8%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 5.00000000000000022e47 < j < 8.0000000000000004e235

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 70.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 70.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 70.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 70.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 70.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 70.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around 0 59.2%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 59.2%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-in 59.2%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   7. Simplified 59.2%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   if 8.0000000000000004e235 < j

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 58.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 46.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 46.1%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Taylor expanded in a around 0 46.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. *-commutative 46.1%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot a \]

      3. associate-*l* 57.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

      4. *-commutative 57.5%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   10. Simplified 57.5%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+235}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 22: 29.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+260}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+166}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{+56} \lor \neg \left(z \leq 4.8 \cdot 10^{-80}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.9e+260)
   (* y (* x z))
   (if (<= z -2.1e+166)
     (* c (* z (- b)))
     (if (or (<= z -3.65e+56) (not (<= z 4.8e-80)))
       (* x (* y z))
       (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.9e+260) {
		tmp = y * (x * z);
	} else if (z <= -2.1e+166) {
		tmp = c * (z * -b);
	} else if ((z <= -3.65e+56) || !(z <= 4.8e-80)) {
		tmp = x * (y * z);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.9d+260)) then
        tmp = y * (x * z)
    else if (z <= (-2.1d+166)) then
        tmp = c * (z * -b)
    else if ((z <= (-3.65d+56)) .or. (.not. (z <= 4.8d-80))) then
        tmp = x * (y * z)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.9e+260) {
		tmp = y * (x * z);
	} else if (z <= -2.1e+166) {
		tmp = c * (z * -b);
	} else if ((z <= -3.65e+56) || !(z <= 4.8e-80)) {
		tmp = x * (y * z);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.9e+260:
		tmp = y * (x * z)
	elif z <= -2.1e+166:
		tmp = c * (z * -b)
	elif (z <= -3.65e+56) or not (z <= 4.8e-80):
		tmp = x * (y * z)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.9e+260)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -2.1e+166)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif ((z <= -3.65e+56) || !(z <= 4.8e-80))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.9e+260)
		tmp = y * (x * z);
	elseif (z <= -2.1e+166)
		tmp = c * (z * -b);
	elseif ((z <= -3.65e+56) || ~((z <= 4.8e-80)))
		tmp = x * (y * z);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.9e+260], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e+166], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.65e+56], N[Not[LessEqual[z, 4.8e-80]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8999999999999999e260

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 72.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 72.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 72.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 72.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 72.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 72.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around inf 78.6%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -1.8999999999999999e260 < z < -2.1000000000000001e166

   1. Initial program 61.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 62.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 62.1%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 62.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in z around inf 70.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 70.0%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 70.0%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 70.0%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   7. Simplified 70.0%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-neg-out 70.0%

         \[\leadsto \color{blue}{-b \cdot \left(z \cdot c\right)} \]

      2. add-sqr-sqrt 46.4%

         \[\leadsto -\color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot \left(z \cdot c\right) \]

      3. sqrt-unprod 39.1%

         \[\leadsto -\color{blue}{\sqrt{b \cdot b}} \cdot \left(z \cdot c\right) \]

      4. sqr-neg 39.1%

         \[\leadsto -\sqrt{\color{blue}{\left(-b\right) \cdot \left(-b\right)}} \cdot \left(z \cdot c\right) \]

      5. sqrt-unprod 0.0%

         \[\leadsto -\color{blue}{\left(\sqrt{-b} \cdot \sqrt{-b}\right)} \cdot \left(z \cdot c\right) \]

      6. add-sqr-sqrt 1.1%

         \[\leadsto -\color{blue}{\left(-b\right)} \cdot \left(z \cdot c\right) \]

      7. associate-*r* 1.1%

         \[\leadsto -\color{blue}{\left(\left(-b\right) \cdot z\right) \cdot c} \]

      8. add-sqr-sqrt 0.0%

         \[\leadsto -\left(\color{blue}{\left(\sqrt{-b} \cdot \sqrt{-b}\right)} \cdot z\right) \cdot c \]

      9. sqrt-unprod 39.1%

         \[\leadsto -\left(\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}} \cdot z\right) \cdot c \]

      10. sqr-neg 39.1%

          \[\leadsto -\left(\sqrt{\color{blue}{b \cdot b}} \cdot z\right) \cdot c \]

      11. sqrt-unprod 46.4%

          \[\leadsto -\left(\color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot z\right) \cdot c \]

      12. add-sqr-sqrt 70.3%

          \[\leadsto -\left(\color{blue}{b} \cdot z\right) \cdot c \]

   9. Applied egg-rr 70.3%

      \[\leadsto \color{blue}{-\left(b \cdot z\right) \cdot c} \]

   if -2.1000000000000001e166 < z < -3.65e56 or 4.7999999999999998e-80 < z

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 53.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.9%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 53.9%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 53.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 38.6%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 38.6%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if -3.65e56 < z < 4.7999999999999998e-80

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 58.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 58.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 37.1%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 37.1%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 37.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 37.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 36.2%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 36.2%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 36.2%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 36.2%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 36.2%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 36.2%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 36.2%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 36.2%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 37.1%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 37.1%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 37.1%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 32.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*l* 34.2%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   10. Simplified 34.2%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+260}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+166}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{+56} \lor \neg \left(z \leq 4.8 \cdot 10^{-80}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 23: 30.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{+83} \lor \neg \left(c \leq 4.05 \cdot 10^{+65}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.75e+83) (not (<= c 4.05e+65))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.75e+83) || !(c <= 4.05e+65)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.75d+83)) .or. (.not. (c <= 4.05d+65))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.75e+83) || !(c <= 4.05e+65)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.75e+83) or not (c <= 4.05e+65):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.75e+83) || !(c <= 4.05e+65))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.75e+83) || ~((c <= 4.05e+65)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.75e+83], N[Not[LessEqual[c, 4.05e+65]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.7499999999999998e83 or 4.05e65 < c

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 53.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 53.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 42.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.1%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 42.1%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -2.7499999999999998e83 < c < 4.05e65

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 48.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 48.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 34.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 34.3%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 34.3%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 34.3%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 34.3%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 34.3%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 34.3%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 34.3%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 34.3%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 34.3%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 34.3%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 34.3%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 34.3%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 34.3%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 34.3%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 34.3%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 34.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 23.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{+83} \lor \neg \left(c \leq 4.05 \cdot 10^{+65}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 24: 28.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+51} \lor \neg \left(z \leq 3 \cdot 10^{-79}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -1.4e+51) (not (<= z 3e-79))) (* x (* y z)) (* t (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -1.4e+51) || !(z <= 3e-79)) {
		tmp = x * (y * z);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-1.4d+51)) .or. (.not. (z <= 3d-79))) then
        tmp = x * (y * z)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -1.4e+51) || !(z <= 3e-79)) {
		tmp = x * (y * z);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -1.4e+51) or not (z <= 3e-79):
		tmp = x * (y * z)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -1.4e+51) || !(z <= 3e-79))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -1.4e+51) || ~((z <= 3e-79)))
		tmp = x * (y * z);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -1.4e+51], N[Not[LessEqual[z, 3e-79]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000002e51 or 3e-79 < z

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 53.8%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 53.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 40.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 40.4%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if -1.40000000000000002e51 < z < 3e-79

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 58.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 58.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 37.1%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 37.1%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 37.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 37.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 36.2%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 36.2%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 36.2%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 36.2%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 36.2%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 36.2%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 36.2%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 36.2%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 37.1%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 37.1%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 37.1%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 32.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*l* 34.2%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   10. Simplified 34.2%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+51} \lor \neg \left(z \leq 3 \cdot 10^{-79}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 25: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.02 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.02e+80)
   (* j (* a c))
   (if (<= c 3.8e+64) (* b (* t i)) (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.02e+80) {
		tmp = j * (a * c);
	} else if (c <= 3.8e+64) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-2.02d+80)) then
        tmp = j * (a * c)
    else if (c <= 3.8d+64) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.02e+80) {
		tmp = j * (a * c);
	} else if (c <= 3.8e+64) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.02e+80:
		tmp = j * (a * c)
	elif c <= 3.8e+64:
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.02e+80)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= 3.8e+64)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.02e+80)
		tmp = j * (a * c);
	elseif (c <= 3.8e+64)
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.02e+80], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e+64], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.0199999999999999e80

   1. Initial program 51.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 40.5%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 40.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Taylor expanded in a around 0 40.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. *-commutative 40.5%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot a \]

      3. associate-*l* 42.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

      4. *-commutative 42.2%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   10. Simplified 42.2%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if -2.0199999999999999e80 < c < 3.8000000000000001e64

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 48.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 48.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 34.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 34.3%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 34.3%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 34.3%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 34.3%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 34.3%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 34.3%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 34.3%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 34.3%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 34.3%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 34.3%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 34.3%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 34.3%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 34.3%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 34.3%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 34.3%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 34.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 23.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 3.8000000000000001e64 < c

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 53.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 53.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 53.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 43.5%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 43.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.02 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 26: 29.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.9e-67)
   (* a (* c j))
   (if (<= j 1.05e-53) (* t (* b i)) (* j (* a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.9e-67) {
		tmp = a * (c * j);
	} else if (j <= 1.05e-53) {
		tmp = t * (b * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.9d-67)) then
        tmp = a * (c * j)
    else if (j <= 1.05d-53) then
        tmp = t * (b * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.9e-67) {
		tmp = a * (c * j);
	} else if (j <= 1.05e-53) {
		tmp = t * (b * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.9e-67:
		tmp = a * (c * j)
	elif j <= 1.05e-53:
		tmp = t * (b * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.9e-67)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 1.05e-53)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.9e-67)
		tmp = a * (c * j);
	elseif (j <= 1.05e-53)
		tmp = t * (b * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.9e-67], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e-53], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.89999999999999994e-67

   1. Initial program 60.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 52.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 52.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 33.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.8%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 33.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -1.89999999999999994e-67 < j < 1.04999999999999989e-53

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 42.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 42.2%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 42.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 43.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 43.4%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 43.4%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 43.4%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 43.4%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 42.5%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 42.5%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 42.5%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 42.5%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 42.5%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 42.5%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 42.5%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 42.5%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 43.4%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 43.4%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 43.4%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 43.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 24.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 24.8%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 24.8%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*l* 27.8%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   10. Simplified 27.8%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if 1.04999999999999989e-53 < j

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 46.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 46.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 35.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 35.4%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Taylor expanded in a around 0 35.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. *-commutative 35.4%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot a \]

      3. associate-*l* 36.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

      4. *-commutative 36.5%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   10. Simplified 36.5%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 27: 29.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.3e+52)
   (* y (* x z))
   (if (<= z 3e-79) (* t (* b i)) (* x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e+52) {
		tmp = y * (x * z);
	} else if (z <= 3e-79) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.3d+52)) then
        tmp = y * (x * z)
    else if (z <= 3d-79) then
        tmp = t * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e+52) {
		tmp = y * (x * z);
	} else if (z <= 3e-79) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.3e+52:
		tmp = y * (x * z)
	elif z <= 3e-79:
		tmp = t * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.3e+52)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 3e-79)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.3e+52)
		tmp = y * (x * z);
	elseif (z <= 3e-79)
		tmp = t * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.3e+52], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-79], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e52

   1. Initial program 69.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 50.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 50.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 50.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 50.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 50.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around inf 50.5%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -2.3e52 < z < 3e-79

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around 0 58.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   4. Simplified 58.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in j around 0 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 37.1%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. distribute-lft-neg-in 37.1%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      3. sub-neg 37.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)} \]

      4. +-commutative 37.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(-i \cdot t\right) + c \cdot z\right)} \]

      5. distribute-lft-in 36.2%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-i \cdot t\right) + \left(-b\right) \cdot \left(c \cdot z\right)} \]

      6. distribute-rgt-neg-in 36.2%

         \[\leadsto \color{blue}{\left(-\left(-b\right) \cdot \left(i \cdot t\right)\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      7. neg-mul-1 36.2%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot \left(i \cdot t\right)\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      8. associate-*r* 36.2%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      9. mul-1-neg 36.2%

         \[\leadsto \left(-\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + \left(-b\right) \cdot \left(c \cdot z\right) \]

      10. remove-double-neg 36.2%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + \left(-b\right) \cdot \left(c \cdot z\right) \]

      11. distribute-lft-neg-in 36.2%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} \]

      12. distribute-rgt-neg-in 36.2%

          \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      13. distribute-lft-in 37.1%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      14. sub-neg 37.1%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. *-commutative 37.1%

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   8. Taylor expanded in i around inf 32.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*l* 34.2%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   10. Simplified 34.2%

       \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if 3e-79 < z

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in x around inf 53.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.4%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 53.4%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   4. Simplified 53.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   5. Taylor expanded in z around inf 35.3%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Simplified 35.3%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 28: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

2. Taylor expanded in a around inf 40.7%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
3. Step-by-step derivation

   1. +-commutative 40.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.7%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

4. Simplified 40.7%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

5. Taylor expanded in c around inf 21.9%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
6. Step-by-step derivation

   1. *-commutative 21.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

7. Simplified 21.9%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Final simplification 21.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 58.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))